CN106773673A - A kind of magnetic suspension rotor method for inhibiting harmonic current of the fractional compensation repetitive controller based on frequency self adaptation - Google Patents
A kind of magnetic suspension rotor method for inhibiting harmonic current of the fractional compensation repetitive controller based on frequency self adaptation Download PDFInfo
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Abstract
The invention discloses a kind of magnetic suspension rotor method for inhibiting harmonic current of the fractional compensation repetitive controller based on frequency self adaptation.Initially set up the magnetic suspension rotor kinetic model comprising unbalance mass, and sensor harmonic wave, secondly consider that low pass filter Q (s) causes the amplitude attenuation and delayed phase of high frequency band signal, rejection ability of the reduction system to disturbance, by low pass filter Q (s) by the branch road that repetitive controller is moved in backfeed loop, fractional order compensation tache is substituted by fraction filtering wave by prolonging time device, by the online updating of fraction filtering wave by prolonging time device coefficient, it is possible to achieve the harmonic current under optional frequency accurately suppresses.The present invention can realize the accurate suppression of the harmonic current of magnetically levitated flywheel or magnetic suspension wipping top under any rated speed, it is adaptable to which the electric current that there is the magnetic suspension rotor harmonic wave of mass unbalance and sensor harmonic wave suppresses.
Description
Technical field
The present invention relates to the technical field of magnetic suspension rotor current harmonics elimination, and in particular to one kind based on integer time delay with
The magnetic suspension rotor method for inhibiting harmonic current that fractional order repetitive controller is combined, flies for magnetic suspension wipping top or magnetic suspension
The application that the current harmonics elimination of wheel is magnetically levitated flywheel or gyro on " super quiet " satellite platform provides technical support.
Background technology
Magnetic suspension rotor using magnetic bearing support by the way of, due to magnetic axis bearing rotor system have the long-life, without friction and
The advantages of active vibration is controllable, it is adaptable to various high-speed rotating equipments, in space flight, aviation, core cause and mechanical engineering field etc.
Field is with a wide range of applications, and particularly has good at aspects such as magnetically levitated flywheel, magnetic suspension wipping top and maglev molecular pumps
Good application.
In a practical situation, due to the influence of the factor such as machining accuracy finite sum material is uneven, magnetic suspension rotor
It is unavoidable that mass unbalance occurs, can be produced during high-speed rotation and be disturbed with frequency with speed-frequency identical；Separately
On the one hand, because sensor detection faces, detection surface electric or magnetic characteristic are inconsistent, the disturbing signal with frequency and frequency multiplication can be produced,
Sensor harmonic wave is that is to say, sensor harmonic wave can trigger harmonic controling electric current.Harmonic controling electric current and then initiation magnetic bearing generation
Harmonic vibration power, vibration is delivered to pedestal and then passes to spacecraft by magnetic bearing, influences spacecraft pointing accuracy and stabilization
Precision.
In current harmonics elimination algorithm, can multi-frequency composition be suppressed according to algorithm simultaneously, can be classified as with
Lower two classes：One class is that single-frequency suppresses, and carries out suppressing to need the folded of such algorithm to the harmonic signal to multi-frequency composition
Plus, multiple trappers such as in parallel or multiple LMS wave filters.The method complexity and computationally intensive, and different frequency need to be considered
Disturbance Rejection convergence of algorithm speed, harmonics restraint performance is low, is unfavorable for engineering application.Another kind of algorithm is need not multiple
Algorithm it is cumulative, single algorithm is to suppress while being capable of achieving to multi-frequency constituent fluctuation, that is to say repetitive control.Weight
Multiple control algolithm is based on internal model principle, can to known to the cycle, amplitude do not know, the periodic disturbance comprising multi-frequency composition
Signal is effectively suppressed, and essence is implanted to inside controller by by the equivalent mathematical model of external signal, so that real
Now to external input signal tracking or inhibitory action.Repetitive control have small amount of calculation, simple structure, committed memory small and
The advantages of being easily achieved, it is adaptable to the suppression of the various frequencys multiplication of active magnet bearing systems.Repetitive control as shown in Figure 4, only
Electric current suppression can be carried out for specific rotor speed, once sample frequency is not integer with the ratio of harmonic interference signals fundamental frequency
When, it is impossible to fractional part is compensated, that is to say cannot accomplish under any rated frequency to the accurate of harmonic disturbance signal
Suppress.
The content of the invention
The purpose of the present invention：Overcome the shortcomings of existing traditional controller, invention one kind is not limited by low pass filter, and
In the case of the ratio of sample frequency and harmonic current fundamental frequency is for fraction, the frequency adaptive fractional rank that can be compensated repeats to control
Algorithm processed.
Technical solution of the invention：A kind of magnetic suspension of the fractional compensation repetitive controller based on frequency self adaptation turns
Sub- method for inhibiting harmonic current, it is characterised in that comprise the following steps：
Step (1) sets up the magnetic suspension rotor kinetic model comprising unbalance mass, and sensor harmonic wave
According to Newton's second law, magnetic suspension rotor is in the kinetics equation of X-direction：
Wherein,Acceleration of the rotor in X-direction is represented, m represents rotor quality, fxRepresent bearing of the magnetic bearing in X-direction
Power, fuThe out-of-balance force of rotor is represented, is represented by：
fu=me Ω2cos(Ωt+φ)
Wherein e represents the deviation between rotor geometric center and barycenter, and Ω represents rotor speed, and φ represents rotor unbalance
The initial phase of quality；
When rotor suspends around magnetic bearing center, the electromagnetic force of magnetic bearing is represented by lienarized equation：
fx≈Kxx+Kii
Wherein KxAnd KiMagnetic bearing displacement rigidity and current stiffness are represented respectively, and i represents magnetic bearing coil control electric current；
Due to the influence of machining accuracy and the uneven factor of material, the displacement transducer detection faces of magnetic suspension rotor
Occur that circularity is undesirable, material is uneven, the different factors of remanent magnetism, the output of displacement transducer will occur with frequently and again
The multiple-harmonic signal of frequency, the then output of displacement transducer is represented by：
xs(t)=x (t)+xd(t)
Wherein x (t) represents the real coordinate value of rotor geometric center, xsT () represents the output valve of sensor, xdT () is biography
Sensor output valve and the error of actual value, are represented by：
Wherein l represents overtone order, clRepresent harmonic constant, θlRepresent harmonic wave initial phase；
By i, xd(t)、fuCarrying out Laplace transform successively can obtain i (s), xd(s)、fu(s), then magnetic bearing electric current i (s)
Transmission function be represented by：
Wherein GcS () is the transmission function of controller, GwS () is the transmission function of power amplifier link, GpS () is that magnetic suspension turns
The transmission function of son, wherein R (s) represents reference-input signal, KsRepresent sensor gain；
Step (2)：The foundation of the fractional compensation repetitive controller based on frequency self adaptation
The ratio that N is system sampling frequency and harmonic signal fundamental frequency is defined, while the size of N reflects fraction to repeat to control
The height of the control resolution of device processed, general sample frequency is higher to mean that control accuracy is higher.In practical implementation, point
Number time delay process cannot be directly realized by, it is necessary to find a kind of alternative forms.Fractional order time delay processCan be bright with a kind of glug
Day interpolation polynomial is substituted；
Step (3)：The stability analysis of the fractional compensation repetitive controller based on frequency self adaptation
For the ease of the stability analysis of system, R (ω) is composed in the reconstruct for introducing repetitive controller.Reconstruct spectral function is used as sentencing
A kind of foundation of the disconnected stability of a system：According to knowable to least gain is theoretical, for a systems stabilisation, if adding Repetitive controller
System reconfiguration spectral function can meet R (ω) after device<1, then new system is also stabilization.
Step (4)：The son of the current harmonics elimination algorithm of fractional compensation repetitive controller of the design based on frequency self adaptation
Step
When the ratio of system sampling frequency and harmonic signal fundamental frequency is not integer, in order to realize the benefit to fractional part
Repay, as shown in figure 5, with from Gw(s) output electric current i as repetitive controller input, by integer time delay and fraction time delay
The frequency adaptive fractional compensation repetitive controller being in series, the output of repetitive controller and controller GcS the output of () is together
As GwThe input of (s), while by low pass filter Q (s) by moving to the branch being in series with repetitive controller in backfeed loop
Lu Shang.Using system above structure, the influence that low pass filter amplitude attenuation and delayed phase bring on the one hand is eliminated, made
The system of obtaining can also realize that electric current suppresses in high band, not be on the other hand whole with harmonic disturbance signal fundamental frequency ratio in sample frequency
During number, it is possible to achieve fractional order is compensated, so as to improve the current harmonics elimination precision of magnetic bearing under any rated speed.
Using outside reference-input signal R (s) harmony wave disturbance equivalent signal D (s) as input, with magnetic bearing coil current
I (s) adds sensitivity function S during fractional order repetitive controller as output2S () can be expressed as follows：
Wherein,Represent the sensitivity function of system when not adding repetitive controller, N1
Represent the complete cycle issue of sampling, N2Leading phase compensation periodicity is represented, A represents decimal compensation cycle number, and N=N1+N2+
A, illustrates, when N is fraction, can also cause sensitivity function S2S () amplitude is zero, and do not influenceed by low pass filter.Kf
S () is phase compensation function and KrcIt is gain-adjusted parameter, the cut-off frequency ω of low pass filter Q (s)cDisturbed more than effective harmonic wave
Dynamic highest frequency ωmax, in ω ∈ (0, ωmax) in the range of Q (s) amplitude attenuation and delayed phase very little, | Q (s) | ≈ 1,
arg[Q(s)]S=j ω≈0。
Further, step (2) the fractional order time delay process is represented by：
It is the integer time delay process in sampling period,The phase lead compensation link of repetitive controller.Due toAnd N1+N2=int [N] as N integer part, so there is A=N- (N1+N2), 0 ＜ A ＜ 1 make
It is the fractional part of N.Fractional order time delay processCan be represented with a kind of Lagrange interpolation polynomial：
Wherein coefficient DlCan be expressed as follows：
Its general principles：Due to mass unbalance and the presence of sensor harmonic wave, active magnetic bearings can produce harmonic wave
Electric current, so as to cause harmonic vibration, influences the working condition of magnetic suspension rotor.The present invention is suppressed for harmonic current, is subtracted
Small harmonic vibration.By setting up the magnetic suspension rotor kinetic model containing mass unbalance and sensor harmonic wave, analysis system
Harmonic current, it is proposed that a kind of fractional compensation repetitive controller of frequency self adaptation, so as under realizing magnetic suspension rotor rotating speed high
Current harmonics elimination, emphasis is studied in terms of two：The design of fractional order time delay process, introduces fraction filtering wave by prolonging time device and replaces
For fraction time delay process, when the rotating speed of rotor changes, can be by the online coefficient for changing fraction filtering wave by prolonging time device
Realize that fractional part is accurately compensated；By designed phase compensation tache to ensure stability, magnetcisuspension under any rotating speed is finally realized
The accurate suppression of floating rotor harmonic current.
Present invention advantage compared with prior art is：Low pass filter is moved to and repetition control from backfeed loop
On the branch road that device processed is in series, effectively eliminate due to the influence that low pass filter amplitude attenuation and delayed phase bring, drawn
Enter fractional compensation link so that system has and has balanced ability to fraction so that system can be in any specified sample frequency
Under, the accurate suppression to harmonic disturbance signal can be realized.
Brief description of the drawings
Fig. 1 is flow chart of the invention；
Fig. 2 is magnetic suspension rotor system structural representation, wherein, 1 is magnetic bearing, and 2 is rotor, and 3 is the principal axis of inertia, and 4 are
Geometrical axis；
Fig. 3 is X passage magnetic bearing rotor control system block diagram；
Fig. 4 is traditional repetitive controller system block diagram；
Fig. 5 is fractional order repetitive controller system block diagram；
Fig. 6 is the improvement repetitive controller system block diagram after simplifying；
Fig. 7 is current harmonics elimination result of the magnetic bearing rotor under 75Hz.Wherein Fig. 7 a are to be not added with vibration suppression algorithm,
Fig. 7 b are the repetitive controller for adding the method for the invention.
Specific embodiment
Below in conjunction with the accompanying drawings and instantiation further illustrates the present invention.
As shown in figure 1, a kind of magnetic suspension rotor harmonic current of the fractional compensation repetitive controller based on frequency self adaptation
The implementation process of suppressing method is：The magnetic suspension rotor kinetic model containing mass unbalance and sensor harmonic wave is initially set up,
Then a kind of magnetic suspension rotor method for inhibiting harmonic current of the fractional compensation repetitive controller based on frequency self adaptation is designed.
Magnetic suspension rotor system is by displacement transducer Ks, controller Gc(s), power amplifier Gw(s) and magnetic suspension rotor Gp
S () constitutes, displacement sensor goes out rotor displacement and feed back to controller, controller output control amount to power amplifier,
To magnetic bearing coil, magnetic bearing generation power and torque make rotor stability suspend to power amplifier output current.Due to machining
Limited precision, magnetic suspension rotor is unavoidable to occur mass unbalance；Due to sensor detection faces, detection surface electric or magnetic
Characteristic is inconsistent, can produce the disturbing signal with frequency and frequency multiplication, that is to say sensor harmonic wave.
Step (1) sets up the Mathematical Modeling of the magnetic suspension rotor comprising unbalance mass, and sensor harmonic wave
Except being freely outside one's consideration by the axial-rotation of motor control, other five frees degree are by active magnetic to magnetic suspension rotor
Bearing is controlled.Its system structure diagram is as shown in Fig. 2 two translations of radial passage are by active magnetic bearings control.C is represented
The barycenter of rotor, N represents the geometric center of magnetic bearing stator, and inertial coodinate system NXY is set up centered on N.O represents the several of rotor
What center, sets up rotating coordinate system O ε η centered on O.Because rotor structure is symmetrical, so rotor has phase in X and Y-direction
Same Mathematical Modeling, according to Newton's second law, magnetic suspension rotor is in the kinetics equation of X-direction：
Wherein,Acceleration of the rotor in X-direction is represented, m represents rotor quality, fxRepresent bearing of the magnetic bearing in X-direction
Power, fuThe out-of-balance force of rotor is represented, is represented by：
fu=me Ω2cos(Ωt+φ)
Wherein e represents the deviation between rotor geometric center and barycenter, and Ω represents rotor speed, and φ represents rotor unbalance
The initial phase of quality；
When rotor suspends around magnetic bearing center, the electromagnetic force of magnetic bearing rotor is represented by lienarized equation：
fx≈Kxx+Kii
Wherein KxAnd KiMagnetic bearing displacement rigidity and current stiffness are represented respectively, and i represents magnetic bearing coil control electric current；
Due to the influence of the factor such as uneven of machining accuracy and material, the displacement transducer detection of magnetic suspension rotor
Face occurs that circularity is undesirable, material is uneven, the not equal factor of remanent magnetism, and the output of displacement transducer will occur with frequency
With the multiple-harmonic signal of frequency multiplication, then the output of displacement transducer is represented by：
xs(t)=x (t)+xd(t)
Wherein x (t) represents the real coordinate value of rotor geometric center, xsT () represents the output valve of sensor, xdT () is biography
Sensor output valve and the error of actual value, are represented by：
Wherein l represents overtone order, clRepresent harmonic constant, θlRepresent harmonic wave initial phase.In formula, as l=1, represent
There is homogenous frequency signal in displacement transducer output, and as l=2,3,4......., comprising frequency multiplication letter in expression displacement transducer
Number, that is to say in system there is multiple harmonic.
Magnetic suspension rotor kinetics equation in the Y direction is：
Wherein,Rotor acceleration in the Y direction is represented, m represents rotor quality, fyRepresent magnetic bearing bearing in the Y direction
Power, fuThe out-of-balance force of rotor is represented, is represented by：
fu=me Ω2cos(Ωt+φ)
Wherein e represents the deviation between rotor geometric center and barycenter, and Ω represents rotor speed, and φ represents rotor unbalance
The initial phase of quality；
When rotor suspends around magnetic bearing center, the electromagnetic force of magnetic bearing rotor is represented by lienarized equation：
fy≈Kyy+Kii
Wherein KyAnd KiMagnetic bearing displacement rigidity and current stiffness are represented respectively, and i represents magnetic bearing coil control electric current；
The then output of displacement transducer is represented by：
ys(t)=y (t)+yd(t)
Wherein y (t) represents the real coordinate value of rotor geometric center, ysT () represents the output valve of sensor, ydT () is biography
Sensor output valve and the error of actual value, are represented by：
Wherein l represents overtone order, clRepresent harmonic constant, θlRepresent harmonic wave initial phase.In formula, as l=1, represent
There is homogenous frequency signal in displacement transducer output, and as l=2,3,4......., comprising frequency multiplication letter in expression displacement transducer
Number, that is to say in system there is multiple harmonic.
By i, xd(t)、fuCarrying out Laplace transform successively can obtain i (s), xd(s)、fu(s).From figure 3, it can be seen that now
Not plus repetitive control, it is input with external reference signal R (s), by only by Gc(s)、Gw(s)、Gp(s) and KsFeed back to
The system of road composition, final output signal has also been superimposed fuAnd xd(t)/ydT output that () causes, it can thus be concluded that magnetic bearing electric current i
S the transmission function of () is represented by：
Or
Wherein GcS () is the transmission function of controller, GwS () is the transmission function of power amplifier link, GpS () is that magnetic suspension turns
The transmission function of son, wherein R (s) represents reference-input signal, KsRepresent sensor gain；
Analysis can be obtained with reference to more than, and rotor quality is uneven and sensor error can cause that magnetic bearing produces harmonic controling
Electric current, so as to produce harmonic vibration.
Step (2)：The foundation of the fractional compensation repetitive controller based on frequency self adaptation
The ratio that N is system sampling frequency and harmonic signal fundamental frequency is defined, while the size of N reflects fractional order repetition
The height of the control resolution of controller, general sample frequency is higher to mean that control accuracy is higher.Due toAnd N1+N2=int [N] as N integer part, so there is A=N- (N1+N2), 0 ＜ A ＜ 1 make
It is the fractional part of N.In practical implementation, fraction time delay process cannot be directly realized by, it is necessary to find a kind of alternative forms.
Fractional order time delay processCan be represented with a kind of Lagrange interpolation polynomial：
Wherein coefficient DlCan be expressed as follows：
According to lagrange-interpolation, multinomialWith fraction time delay processDifference RnCan represent such as
Under：
Wherein ξ ∈ [Tk,Tk+1], TkAnd Tk+1Represent respectively k-th and kth+1 sampling instant, with Lagrange insert
The increase of value polynomial order n, approximate remainder RnIt is gradually reduced, i.e. the degree of approximation of Lagrange interpolation polynomial gradually rises
Height, but, with the increase of n, algorithm amount of calculation will significantly increase.In Practical Project, it should consider difference RnWith
Two factors of algorithm amount of calculation, select n=1 in the present invention, then have
The stability analysis of the fractional compensation of fractional compensation repetitive controller of the step (3) based on frequency self adaptation
After introducing fractional order compensation tache, in ω ∈ (0, ωc) in frequency range, fractional order time delay processCan use
A kind of Lagrange interpolation polynomial represents, namelyPolynomial phase is-ATsω, amplitude isStability analysis is carried out to system after algorithm is added, can be obtained as follows：
As ω ∈ (0, ωc) when, as shown in figure 5, introducing fractional compensation link, mutually gone here and there with fraction time delay using integer time delay
The frequency adaptive fractional compensation repetitive controller of connection, and adds corresponding phase compensation function, while by low pass filter Q
S () in backfeed loop by moving on the branch road being in series with repetitive controller.Fig. 5 obtains Fig. 6, Fig. 6 mid-scores by simplification
Time delay process is substituted by fraction filtering wave by prolonging time device, and withThe phase compensation of high band is in series, wherein phase compensation
Function C (s) can be expressed as：
Wherein KrcRepresent and improve repetitive controller gain, KfS () is represented in low-frequency range and the phase compensation function of Mid Frequency,Represent the phase compensation function of high band.
The closed loop transform function that addition improves system after repetitive controller can be obtained by Fig. 6, be expressed as follows：
Wherein, M (s)=1+Gc(s)Gw(s)Gp(s)Ks,
For the ease of the stability analysis of system, the reconstruct spectrum after improving repetitive controller is introduced, reconstruct the definition of spectrum such as
Under：
Reconstruct spectral function can be as a kind of foundation for judging the stability of a system：According to knowable to least gain is theoretical, for
One systems stabilisation, if system reconfiguration spectral function can meet R (ω) ＜ 1, ω ∈ (0, ω after adding repetitive controllerc), then
New system is also stabilization.
Define system function F (s)：
Wherein, | F (s) |S=j ω=L (ω) ejθ(ω), the reconstruct spectral function of system is after addition repetitive controller：
WhereinTake λ (ω)=θ (ω)+θb(ω)+(N2+A)Tsω, above formula passes through
Euler's formula can be obtained：
|1+KrcL(ω)·Kb(ω)cosλ(ω)+jKrcL(ω)·Kb(ω) sin λ (ω) | ＜ 1
Above formula both sides are carried out respectively modulus square, can obtain：
[KrcL(ω)·Kb(ω)]2＜ -2KrcL(ω)·Kb(ω)cosλ(ω)
Because the gain K of repetitive controllerrc＞ 0, and L (ω) ＞ 0, Kb(ω) ＞ 0, institute's above formula can be reduced to：
KrcL(ω)·Kb(ω) ＜ -2cos λ (ω)
Cause that above formula is permanent to set up, it is necessary to assure cos λ (ω) ＜ 0, that is to say：
90 ° of 270 ° of ＜ λ (ω) ＜
In sum, by suitable phase compensation function and the gain coefficient of connecting, it is ensured that add system after algorithm
Stability.
The sub-step of the current harmonics elimination algorithm of step (4) fractional compensation repetitive controller of the design based on frequency self adaptation
Suddenly
Repetitive controller is based on internal model principle, can eliminate the harmonic component in input signal, in actual magnetic bearings control
In system, sample frequency differs with the ratio of harmonic interference signals fundamental frequency and is set to integer, so as to need that fractional part is mended
Repay, the existing repetitive controller for magnetic bearing current harmonics elimination can only be compensated to its integer part, so that
The precision of current harmonics elimination is substantially reduced, not enough for this, and the present invention is in series frequently using integer time delay and fraction time delay
Rate adaptive fractional compensates repetitive controller.As shown in figure 5,It is the integer time delay process in sampling period,Repeat
The phase lead compensation link of controller,It is the fractional order time delay process in sampling period, is substituted by fraction filtering wave by prolonging time device
Obtain.With from GwS the electric current i of () output is in series as the input of repetitive controller by integer time delay and fraction time delay
Frequency adaptive fractional compensates repetitive controller, the output of repetitive controller and controller GcS the output of () is together as Gw(s)
Input, while by low pass filter Q (s) by being moved in backfeed loop on the branch road being in series with repetitive controller.Fraction
Compensation tache is substituted by fraction filtering wave by prolonging time device, when harmonic current fundamental frequency changes, a new decimal can be obtained, small
Number bring the coefficient that fraction filtering wave by prolonging time device determines fraction filtering wave by prolonging time device into, so as to realize fraction filtering wave by prolonging time device coefficient more
Newly, and then can realize compensating fractional part.Using the cascade of the above, on the one hand eliminate low pass filter amplitude and decline
Subtract the influence brought with delayed phase so that system high band can also realize electric current suppress, on the other hand sample frequency with
When harmonic disturbance signal fundamental frequency ratio is not integer, it is possible to achieve fractional order is compensated, so as to improve magnetic axis under any rated speed
The current harmonics elimination precision held, realizes that the magnetic bearing harmonic current under any rated speed accurately suppresses.
Using outside reference-input signal R (s) harmony wave disturbance equivalent signal D (s) as input, now magnetic bearing coil is electric
Stream i (s) is used as the sensitivity function S for exporting2S () can be expressed as follows：
Wherein,The sensitivity function of the system not plus before repetitive controller is represented,
N1Represent the complete cycle issue of sampling, N2Leading phase compensation periodicity is represented, A represents decimal compensation cycle number, and N=N1+N2
+ A, illustrates, when N is fraction, can also cause sensitivity function S2S () amplitude is zero, and do not influenceed by low pass filter.Kf
S () is phase compensation function and KrcIt is gain-adjusted parameter, the cut-off frequency ω of low pass filter Q (s)cDisturbed more than effective harmonic wave
Dynamic highest frequency ωmax, in ω ∈ (0, ωmax) in the range of Q (s) amplitude attenuation and delayed phase very little, | Q (s) | ≈ 1,
arg[Q(s)]s=jω≈0。
Harmonic current frequency domain and result in time domain of the magnetic bearing rotor in the case where rotating speed is 4500rpm (75Hz) are as shown in fig. 7, adopt
Repetitive controller is compensated compared with traditional repetitive controller with frequency adaptive fractional of the invention, and the inhibition of electric current is bright
Aobvious raising.To be not added with map of current during repetitive controller, Fig. 7 (b) is addition fractional order repetitive controller of the invention to Fig. 7 (a)
Electric current inhibition figure.Magnetic bearing is electric before and after can knowing addition fractional order repetitive controller by comparison diagram 7 (a) and Fig. 7 (b)
Stream time domain situation of change：12.4mA is dropped to from 87mA, 85.7% is reduced；Frequency domain situation of change：With frequency (be reduced to from -22dB -
99.7%) 73dB, reduce, and two frequencys multiplication (are reduced to -75dB, reduce 96.8%), frequency tripling is (from -48dB reductions from -45dB
To -71dB, reduce 92.9%), quadruple (is reduced to -77dB, reduces 88.8%), fifth harmonic is (from -57dB from -58dB
- 76dB is reduced to, is reduced 88.8%), from the above analysis, add fractional order repetitive controller effectively to suppress each
The harmonic current of individual frequency range, institute is concise effective in the process of the present invention.
Non-elaborated part of the present invention belongs to prior art known to those skilled in the art.
Claims (1)
1. a kind of magnetic suspension rotor method for inhibiting harmonic current of the fractional compensation repetitive controller based on frequency self adaptation, it is special
Levy and be：Comprise the following steps：
Step (1)：Set up the magnetic suspension rotor kinetic model comprising unbalance mass, and sensor harmonic wave
According to Newton's second law, magnetic suspension rotor is in the kinetics equation of X-direction：
Wherein,Acceleration of the rotor in X-direction is represented, m represents rotor quality, fxRepresent bearing of the magnetic bearing in X-direction, fu
The out-of-balance force of rotor is represented, is represented by：
fu=me Ω2cos(Ωt+φ)
Wherein e represents the deviation between rotor geometric center and barycenter, and Ω represents rotor speed, and φ represents rotor unbalance quality
Initial phase；
When rotor suspends around magnetic bearing center, the electromagnetic force of magnetic bearing is represented by lienarized equation：
fx≈Kxx+Kii
Wherein KxAnd KiMagnetic bearing displacement rigidity and current stiffness are represented respectively, and i represents magnetic bearing coil control electric current；
Due to the influence of machining accuracy and the uneven factor of material, the displacement transducer detection faces of magnetic suspension rotor can go out
Existing circularity is undesirable, material is uneven, the different factors of remanent magnetism, and the output of displacement transducer will occur with frequency and frequency multiplication
Multiple-harmonic signal, then displacement transducer output is represented by：
xs(t)=x (t)+xd(t)
Wherein x (t) represents the real coordinate value of rotor geometric center, xsT () represents the output valve of sensor, xdT () is sensor
Output valve and the error of actual value, are represented by：
Wherein l represents overtone order, clRepresent harmonic constant, θlRepresent harmonic wave initial phase；
By i, xd(t)、fuCarrying out Laplace transform successively can obtain i (s), xd(s)、fu(s), the then transmission of magnetic bearing electric current i (s)
Function is represented by：
Wherein GcS () is the transmission function of controller, GwS () is the transmission function of power amplifier link, GpS () is magnetic suspension rotor
Transmission function, wherein R (s) represent reference-input signal, KsRepresent sensor gain；
Step (2)：The foundation of the fractional compensation repetitive controller based on frequency self adaptation
The ratio that N is system sampling frequency and harmonic signal fundamental frequency is defined, while the size of N reflects fraction repetitive controller
Control resolution height, fractional order time delay processCan be substituted with a kind of Lagrange interpolation polynomial：Wherein coefficient DlCan be expressed as follows：
Step (3)：The stability analysis of the fractional compensation repetitive controller based on frequency self adaptation
For the ease of the stability analysis of system, R (ω) is composed in the reconstruct for introducing repetitive controller, and reconstruct spectral function judges that system is steady
Qualitatively foundation：According to knowable to least gain is theoretical, for a systems stabilisation, if adding system reconfiguration after repetitive controller
Spectral function can meet R (ω)<1, then new system is also stabilization；
Step (4)：The sub-step of the current harmonics elimination algorithm of fractional compensation repetitive controller of the design based on frequency self adaptation
When the ratio of system sampling frequency and harmonic signal fundamental frequency is not integer, in order to realize the compensation to its fractional part,
With from GwThe electric current i of (s) output as repetitive controller input, the frequency being in series by integer time delay and fraction time delay from
Adapt to fractional compensation repetitive controller, the output of repetitive controller and controller GcS the output of () is together as GwThe input of (s),
Simultaneously by low pass filter Q (s) by being moved in backfeed loop on the branch road being in series with repetitive controller；Using the above
System architecture, on the one hand eliminates the influence that low pass filter amplitude attenuation and delayed phase bring so that system is in high band
Can realize that electric current suppresses, on the other hand when sample frequency and harmonic disturbance signal fundamental frequency ratio are not integer, it is possible to achieve point
Number rank compensation, so as to improve the current harmonics elimination precision of magnetic bearing under any rated speed；
Using outside reference-input signal R (s) harmony wave disturbance equivalent signal D (s) as input, with magnetic bearing coil current i (s)
As output, sensitivity function S during fractional order repetitive controller is added2S () can be expressed as follows：
Wherein,Represent the sensitivity function of system when not adding repetitive controller, N1Represent
The complete cycle issue of sampling, N2Leading phase compensation periodicity is represented, A represents decimal compensation cycle number, and N=N1+N2+ A, says
It is bright when N be fraction when, can also cause sensitivity function S2S () amplitude is zero, and do not influenceed by low pass filter；KfS () is
Phase compensation function and KrcIt is gain-adjusted parameter, the cut-off frequency ω of low pass filter Q (s)cMore than effective harmonic disturbance
Highest frequency ωmax, in ω ∈ (0, ωmax) in the range of Q (s) amplitude attenuation and delayed phase very little, | Q (s) | ≈ 1, arg [Q
(s)]S=j ω≈0。
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